Question

Question 2 Let PQ be the perpendicular to the line segment XY. Let PQ and XY intersect in the point A. What is the measure of ∠PAY?

Class 6 - Math - Understanding Elementary Shapes Page 100

Answer 1

PQ perpendicular to XY it means PQ and XY intersect and form four angle of 90° .

you can see in figure :
∠PAY + ∠PAX + ∠QAX + ∠QAY = 360°.
due to PQ _|_ XY at A so,
∠PAY = ∠QAY = ∠QAX = ∠QAY
so,
4 × ∠PAY = 360°
∠PAY = 360/4 = 90°

Answer 2

Hi !

PQ perpendicular to XY .
 This means PQ and XY intersect and form four angle each of 90° . 

In the figure attached :-

∠PAY + ∠PAX + ∠QAX + ∠QAY = 360°.

As PQ  ⊥ XY  [ at A ]

so , 
 
∠PAY = ∠QAY = ∠QAX = ∠QAY 

as these angles are equal ;

4∠PAY = 360°

∠PAY = 360/4
          = 90°